Method for Calibrating an Analysis Device, and Associated Device

ABSTRACT

A method of calibration of a device for analyzing at least one element present in a sample, said device including: a detection assembly configured to acquire an image formed by the interference between a light source and said sample; and digital processing means configured to detect a digital position of at least one element in said sample based on said acquired image; said calibration method including the implementation of a plurality of predetermined displacements of said sample with respect to said detection assembly and, for all of said displacements, the detection of a digital position of a same element to determine the digital position and the real position matching model according to the predetermined displacements and to the digital positions of said element after each displacement.

TECHNICAL BACKGROUND

The present disclosure relates to the field of optical analysis ofbiological particles. The biological particles may be microorganismssuch as bacteria, fungi, or yeasts, for example. They may also be cells,multicellular organisms, or any other particle of contaminating particleor dust type.

The invention particularly advantageously applies to position an opticalsystem on a biological particle of interest to improve the measurementsof the physiological characteristics of the biological particle, forexample, by means of Raman spectroscopy.

BACKGROUND

Raman spectroscopy is a non-destructive method for determining thephysiological characteristics of a biological particle. Such a methodexploits the physical phenomenon according to which a medium slightlymodifies the frequency of the light flowing through the medium. Such amodification of the light frequency corresponds to an energy exchangebetween the light ray and the medium, and provides information relativeto the biological particle present in the medium. Raman spectroscopycomprises sending monochromatic light, for example, a laser beam, on thebiologic particle and analyzing the diffused light.

Document WO 2016/075279 describes a method of analysis of a samplecontaining biological particles by means of an imaging systemimplementing a Raman spectroscopy. A detection assembly looks for theposition of a biological particle in a medium. When a particle isselected, the sample and/or the detection assembly is displaced so thatthe laser beam is focused on the biological particle.

To know the displacement instruction to be applied to the sample and/orto the detection assembly with respect to the laser beam, a digitalposition and real position matching model is used to match the measuredposition of the central pixel of the particle in the image and the realdisplacements to be performed.

When the displacement is performed, an analysis assembly fires a laseron the particle and captures the light having interacted with theparticle to determine at least one characteristic of the particle.

Uncertainties, construction defects or defects due to the tolerances ofthe different mechanical and optical parts may altogether result in asignificant inaccuracy of the displacement to be performed to correctlyposition the particle with respect to the analysis assembly. Indeed, afine analysis mode, such as confocal Raman microspectroscopy adapted toa measurement on an individual cell, imposes positioning an objecthaving a size smaller than 1 μm³, the confocal volume, with an objecthaving its characteristic dimension also in the order of one μm³.

The technical problem targeted by the present invention accordingly isto improve the accuracy of the displacement of the sample and/or of thedetection assembly to improve the analysis of a biological particlepresent in a sample.

SUMMARY OF THE DISCLOSURE

To solve the technical problem, the invention provides calibrating themodel for matching digital positions and real position by observing theinfluence of a plurality of displacement instructions on the position ofat least one element in the image originating from the detectionassembly. For this purpose, the invention uses a very fast detectionassembly integrating a simple acquisition with no accurate focusing,associated with a digital reconstruction of the focusing comprising atleast one digital focusing intended to detect an element present in thesample and to rapidly obtain a position of said element.

For this purpose, the invention concerns a method of calibration of adevice for analyzing at least one element present in a sample, saiddevice comprising:

a detection assembly comprising a light source configured to illuminatesaid sample, an optical system configured to collect the light radiationoriginating from said sample, and a planar image sensor configured toacquire a holographic image formed by the interference between areference wave originating from said light source and a wave diffractedby said radiation originating from the sample; and

digital processing means configured to detect a digital position of atleast one element in said sample based on said acquired holographicimage and to calculate a real position of said element according to saiddigital position and to a digital position and real position matchingmodel.

The invention is characterized in that said calibration method comprisesimplementing a plurality of predetermined displacements of said samplewith respect to said optical system and, for each of said displacements,detecting a digital position of a same element to determine said digitalposition and real position matching model according to the predetermineddisplacements and to the digital positions of said elements after eachdisplacement, said detection comprising the steps of:

acquiring an image;

digitally constructing a series of electromagnetic matrices modeling, bydigital propagation of said acquired holographic image, theelectromagnetic wave in planes parallel to the plane of the image sensorand comprised in said sample for a plurality of deviations with respectto said plane;

based on the series of electromagnetic matrices, determining an averagefocusing matrix for said sample and determining the correspondingelectromagnetic matrix Ifmoy;

identifying said same element in the first corresponding electromagneticmatrix Ifmoy, and

determining said digital position of said same element in saidelectromagnetic matrix Ifmoy.

The invention thus enables to generally compensate the optical defectsof the detection assembly and the mechanical defects resulting from thedisplacement between the sample and/or the detection assembly.

The optical system of the detection assembly may advantageously bereused to perform a Raman microspectroscopic analysis since themispositioning between the optical axis of the optical system and thenormal axis of the sample is compensated by the use of the calibratedmatching model according to the invention.

To be able to rapidly determine the matching model, the focusing isdigitally performed from an out-of-focus image associated with a digitalreconstruction of the focusing. Thus, the digital position of theelement is determined from the digitally focused image. As a result, themeasurement instruments are simplified since it is not necessary to usehighly-accurate focusing devices to focus an image in the order of somehundred nanometers.

The matching model of the invention thus enables to rapidly detect witha great accuracy the real position of a particle based on a digitalposition of a particle of an image. The matching model may then be usedto calculate the displacement of the sample with respect to the analysissystem, and thus to accurately focus a laser shot on a particle having aknown position in the image. The positioning difference between the useof a transformation scale and the matrix of the invention is small butit is sufficient to greatly improve the performance of a Ramanspectroscopy, for example.

For a typical example, a laser beam is focused on the (0, 0, 0)coordinates of a three-dimensional digital space. A particle of interestis detected at pixel coordinates (550, 0, 0). By using a transformationscale linked to the theoretical characteristics of the various elementsforming the system, the displacements of the sample may correspond tocoordinates (39.71, 0, 0) in micrometers. With the invention and thecalibration of the matching model, the displacements of the samplecorrespond to coordinates (39.61, −0.23, 0.18) in micrometers.

The invention thus enables to obtain the high positioning accuracyrequired by this type of application, while doing away with too strongor too expensive constraints relative to the design of the instrument.

According to the invention, said position and real position matchingmodel corresponds to a triaxial matrix along three axes of a metricsystem, said step of determining said digital position of said sameelement in said electromagnetic matrix Ifmoy being carried out along anaxis, modeling the position of said element in the depth of said sample,according to said electromagnetic matrix Ifmoy at the average focusingdistance of said sample.

Such an embodiment thus enables to determine the depth of the element inthe sample by using the digital reconstructions of the focusing. Indeed,the focusing maximum on an element of the sample corresponds to anaccurate position in the depth of the sample that can be digitallyestimated.

According to an embodiment, the predetermined displacements areperformed in two opposite directions for each axis of said metricsystem.

This embodiment aims at performing two displacements of oppositedirections per displacement axis to take into account the dissymmetricalbehavior of the displacement, for example implement by the operation ofa stage with stepper motors. Preferably, this embodiment is alsoimplemented with stages which comprise correction members of backlashcorrection type, having the function of correcting this type of error.For example, along a first axis and starting from the central position,the displacement means perform a first 15-micrometer displacement and asecond-15-micrometer displacement. This also results in a total30-micrometer displacement and also in greater variations of theposition of the element. Thus, the determination of the ratio betweenthe digital and real displacements is more accurate.

According to an embodiment, the determination of said digital positionand real position matching model is performed via an average of thevariations of the digital positions of a plurality of elements presentin said holographic image. This embodiment also enables to improve theaccuracy of the ratio between the digital and real displacements.

According to an embodiment, said optical system having an optical axisand performing the conjugation between a focusing plane and a focalplane, the step of acquisition of said holographic image is carried outwhile said optical system is placed with respect to said sample in sucha way that said elements of said sample are not in said focusing plane.

According to an embodiment, before the steps of acquisition of aholographic image to obtain said digital positions of said element, themethod comprises a step of acquisition of a background image, theholographic images obtained during said acquisition steps beingnormalized by said background image.

This embodiment enables to suppress the impurities present on theoptical system or the sensor to improve the sharpness of the acquiredimage for the different predetermined displacements of said samplerelative to said optical system.

According to an embodiment, said element corresponds to a landmark ofsaid sample. For example, a marker may be positioned on or inside of thesample with characteristics clearly distinct from the medium to ease thedetection of the digital position of the marker in the firstelectromagnetic matrix.

According to an embodiment, said element corresponds to a particlepresent in said sample. Such an embodiment enables to reuse theparticles present in the sample to perform the calibration. Thus, it isnot necessary to position a marker in the sample.

According to an embodiment, said step comprising determining saiddigital position of said particle in said electromagnetic matrix Ifmoyis performed by looking for the center of said particle.

Certain particles extend over a plurality of pixels of the image andover a plurality of depth units of the sample, the present embodimentaims at looking for a center of each particle to determine the positionof the particle. Thereby, this embodiment improves the accuracy of theRaman microspectroscopy since this method is all the more accurate asthe focusing is performed on the center of a particle.

According to an embodiment said digital position and real positionmatching model between is formed by considering a plurality of particlespresent in said sample, the digital positions of the particles betweentwo consecutive images being determined by looking for the positions ofthe particles of said two images, by calculating the vectors couplingthe particles two by two and by determining a probable displacementvector corresponding to the most recurrent vector.

Although the use of the particles of the sample enables to suppress thestep of attaching a marker, recognizing the displacement of a specificparticle between two images containing a plurality of particles may bedifficult. To overcome this problem, this embodiment providescalculating the displacement vectors of a plurality of particles todetermine the general displacement of the particles by means of the mostrecurrent vector.

To determine the most recurrent vector, each vector may be previouslyapproximated to mask the inaccuracies in the detection of the set ofvectors. Similarly, to simplify the correlation of the vectors, only aportion of the two images may be considered.

BRIEF DESCRIPTION OF THE DRAWINGS

The way to implement the present invention, as well as the resultingadvantages, will better appear from the description of the followingnon-limiting embodiment, given as an indication, based on theaccompanying drawings, where FIGS. 1 to 4 show:

FIG. 1: a simplified cross-section view of a device for analyzing aparticle present in a sample according to an embodiment of theinvention;

FIG. 2: a simplified representation of a flowchart of the operation ofthe processing means of FIG. 1 according to a first embodiment;

FIG. 3: a simplified representation of a flowchart of the operation ofthe average focused image determination unit of FIG. 2; and

FIG. 4: a representation of the images obtained for five displacementsof the sample of the analysis device of FIG. 1.

DETAILED DESCRIPTION

FIG. 1 illustrates a device 10 for analyzing a particle 11 present in asample 12. Sample 12 is arranged between a light source 13 which isspatially and temporally coherent (for example, a laser) orpseudo-coherent (for example, a light-emitting diode, a laser diode),having an illumination axis A_(ill), and a digital sensor 16 sensitivein the spectral range of light source 13. Preferably, light source 13has a small spectral width, preferably smaller than 200 nm, smaller than100 nm, or even smaller than 25 nm. Such spectral properties providelight source 13 with a time coherence allowing a holographicreconstruction in a range compatible with the encountered positioninguncertainties in the order of some hundred nanometers. The geometry oflight source 13, its apparent size, and its position in space arepreferably selected according to the optical properties of the system(enlargement, size of the source point . . . ) so that the spatialcoherence of light source 13 is not limiting with respect to the timecoherence defined by the spectral width properties provided hereabove.

In the following, reference is made to the central emission wavelengthof light source 13, for example, in the visible range. Light source 13emits a coherent signal Sn oriented on a first surface of the sample,for example, conveyed by a waveguide such as an optical fiber.

Sample 12 is a liquid such as water, a buffer solution, a culture mediumor a reactive medium (comprising or not an antibiotic), containing theparticles 11 to be observed.

As a variation, sample 12 may appear in the form of a solid medium,preferably translucent, such as an agar-agar gelose, having particles 11located inside and on top of it. Sample 12 may also be a gaseous medium.Particles 11 may be located within the medium or at the surface ofsample 12.

Particles 11 may be microorganisms such as bacteria, fungi, or yeasts.They may also be cells, multicellular organisms, or any other particleof contaminating particle or dust type. The size of the observedparticles 11 varies from 500 nanometers to several hundreds ofmicrometers, or even a few millimeters.

Sample 12 is contained in an analysis chamber, vertically delimited by alower plate and an upper plate, preferably parallel planar plates, forexample, conventional microscope plates. The analysis chamber islaterally delimited by an adhesive or by any other tight material. As avariation, the sample may be deposited on a microscope plate or anequivalent support, without being imprisoned in an analysis chamber.

The lower and upper plates are transparent to the wavelength of lightsource 13, the sample and the chamber for example giving way to morethan 50% of the wavelength of light source 13 under a normal incidenceon the lower plate.

Preferably, particles 11 are arranged in sample 12 at the level of theupper plate. The lower surface of the upper plate comprises for thispurpose ligands enabling to bind the particles, for example, polycations(e.g. poly-L-lysine) or antibodies in the case of microorganisms. Thisenables to contain particles 11 within a thickness equal to or close tothe depth of field of the optical system, that is, within a thicknesssmaller than 1 mm (e.g. lens), and preferably smaller than 100micrometers (e.g. microscope lens) Particles 11 may however displace insample 12.

Preferably, the device comprises an optical system 18 for example formedof a microscope lens, for example, a fixed-focus lens, and of a tubelens, arranged in the air. Optical system 18 is optionally equipped witha filter capable of being located in front of the lens or between thelens and the tube lens. Optical system 18 is characterized by itsoptical axis A_(opt), its object plane, also called plane of focus, at adistance from the lens, and its image plane, which is the conjugate ofthe object plane relative to the optical system.

In other words, an object located in the object plane has acorresponding sharp image of this object in the image plane, also calledfocal plane. The optical properties of optical system 18 are fixed (e.g.fixed focus optical system). The object and image planes are ideallyorthogonal to the optical axis and assumed to be such for themathematical models described hereafter.

Image sensor 16 is planar and is located, opposite an upper surface 14of sample 12, in the focal plane or close thereto, to within assemblyand construction errors. Image sensor 16, for example, a planar CCD orCMOS sensor, comprises a periodic two-dimensional grating of elementarysensitive sites, and a proximity electronic system which sets theexposure time and the resetting of the sites, in a way known per se. Theoutput signal of an elementary site is a function of the quantity ofradiation of the spectral range incident on said site during theexposure time. This signal is then converted, for example, by theproximity electronic system, into an image point or “pixel” of a digitalimage.

Image sensor 16 thus generates a digital image in the form of a matrixof C columns and L rows. Each pixel of this matrix, of coordinates (c,l) in the matrix, corresponds in a way known per se to a position ofCartesian coordinates (x(c, l), y(c, l)) in the focal plane of opticalsystem 18, for example, the position of the center of the elementarysensitive site of rectangular shape. Image sensor 16 also comprises anaxis A_(c) normal to the planar surface of image sensor 16 for which theimage Ih originating from image sensor 16 has a minimum deformation withrespect to the observed scene.

Preferably, the pitch and the filling factor of the periodic grating areselected to respect the Shannon-Nyquist criterion regarding the size ofthe observed particles, to define at least two pixels per particle.Thus, image sensor 16 acquires a transmission image of sample 12 in thespectral range of light source 13.

The image Ih acquired by image sensor 16 comprises holographicinformation since it results from the interference between a wave Fidiffracted by particles 11 and a reference wave Fn having crossed sample12 without having interacted therewith.

As described hereabove, in the case of a CMOS or CCD sensor, the digitalimage Ih acquired and stored in digital processing means 25 is anintensity image, the phase information being thus here intensity-coded,with digital image Ih according to relation:

${Ih} = \begin{pmatrix}{{ih}\left( {1,1} \right)} & \ldots & {{ih}\left( {c,1} \right)} & \ldots & {{ih}\left( {C,1} \right)} \\\vdots & \ddots & \vdots & \ddots & \vdots \\{{ih}\left( {1,l} \right)} & \ldots & {{ih}\left( {c,l} \right)} & \ldots & {{ih}\left( {C,l} \right)} \\\vdots & \ddots & \vdots & \ddots & \vdots \\{{ih}\left( {1,L} \right)} & \ldots & {{ih}\left( {c,L} \right)} & \ldots & {{ih}\left( {C,L} \right)}\end{pmatrix}$

As a variation, it is possible to divide the coherent signal Snoriginating from light source 13 into two components, for example, bymeans of a beam splitter. The first component is then used as areference wave and the second component is diffracted by sample 12, theimage in the image plane of optical system 18 resulting from theinterference between the diffracted wave Fi and the reference wave Fn.

The intensity image Ih acquired by image sensor 16 is not focused on aparticle 11 to be observed and the obtaining of information focused on aparticle 11 is digitally achieved by digital processing means 25connected to image sensor 16 to receive the images Ih acquired by thelatter.

“Out of focus” here means that there is no intersection between theplane of focus and the particle 11 which is to be observed. Digitalprocessing means 25 may correspond to a computer, a microcontroller, atouch tablet or a smartphone, or generally any computer system based ona processor capable of receiving data, of processing the data byimplementing computer instructions stored in a computer memory, and ofdelivering and/or storing in a computer memory the result of theprocessing.

Digital processing means 25 may be connected in wired or wirelessfashion to image sensor 16 or by means of a wireless communication.Digital processing means 25 may be associated with a screen to displayintermediate or final results of the method of the invention. As avariation, digital processing means 25 may correspond to an assembly ofa plurality of computer systems with a system dedicated to image sensor16 and other specific systems for the other elements coupled to digitalprocessing means 25.

Light source 13, image sensor 16, and digital processing means 25 form adevice for analyzing at least one particle 11 in sample 12 to obtain theposition of at least one particle of interest 11 in sample 12.

To perform the analysis of a specific particle of interest 11, presentin sample 12, the device also integrates a stage 20 for displacingsample 12. Stage 20 provides a triaxial displacement of axes X, Y, Zbased on stepper motors controlled by a control unit, for example,digital processing means 25, according to a position or displacementinstruction. Stage 20 enables to displace sample 12 with respect tooptical system 18 along an axis Z ideally parallel to optical axisA_(opt) and to displace sample 12 along two other axes X, Y ideallydefining a plane orthogonal to optical axis A_(opt). As a variation,stage 20 may be configured to displace optical system 18 and/or lightsource 13 while sample 12 is fixed.

Thus, displacements along axes X, Y enable to set to the position ofoptical axis A_(opt) on sample 12, and thus the position of a Ramanlaser on sample 12. Further, displacements along axis Z enable to setthe distance between sample 12 and optical system 18, and accordinglythe position of the focal plane (or, equivalently, the position of theconfocal volume) with respect to sample 12.

Ideally, optical axis A_(opt), the mechanical axis Z of displacement ofstage 20, illumination axis A_(ill), the axis A_(c), normal to theplanar surface of sensor 16, and the axis A_(n), normal to the planarsurface of sample 12 should be aligned, but construction errors and thepresence of a clearance may make such alignments imperfect when a greataccuracy is required. A real axis system, different from system X, Y, Z,linked to the image sensor such as X_(n), Y_(n) and Z_(n) where X_(n)and Y_(n) are in the planar surface of sensor 16 and Z_(n) is collinearto axis A_(c), can be defined.

The calculations for digitally reconstructing the wavefront describedhereafter or displacement instructions are based on such an assumption.In reality, there exist misalignments which are corrected by theinvention by means of the calibration of the matching model.

The Raman spectroscopy analysis assembly for example comprises amonochromatic light source 17 and a spectrometer 19. Light source 17preferably corresponds to a laser.

The beam originating from the laser is directed into optical system 18,and thus onto sample 12, for example, by an assembly of mirrors andfilters 28. Optical system 18 enables to focus light source 17 on aspecific position of the sample, the focusing position being settable bydisplacing sample 12 with respect to optical system 18 by means of stage20. As known per se, stage 20 receives a positioning instruction forsample 12, which enables to position the laser shot thereon, whichinstruction is for example communicated to digital processing means 25,particularly the position of a particle detected as described hereabove.In particular, digital processing means 25 determine a digital positionof the particle according to an image processing and converts thedigital position into a real position of the particle in the sample (forexample, in a fixed reference frame linked to the device frame or to thestage in a way known per se), the real position being communicated tothe displacement means as a position instruction. For this purpose,digital processing means 25 use a model for matching a digital position,noted Pn, and a real position, noted Pr. The calibration of the matchingmodel will be described hereafter.

The Raman diffusion of the laser beam in sample 12 is captured byspectrometer 19 by also passing through the assembly of mirrors andfilters 28. The laser and spectrometer 19 are connected to digitalprocessing means 25, which control the laser shot and receive the imageof the diffusion. Of course, the different elements may be arrangeddifferently without modifying the invention.

The position of optical system 18 and the displacements of sample 12 aimat focusing the laser beam on a particle of interest 11 present insample 12. For this purpose, FIG. 2 illustrates the computer processingunits 51-56, integrated in digital processing means 25 in the form ofcomputer instructions implemented by the computer, after the acquisition50 of the intensity image Ih by image sensor 16. A first unit 51constructs a series of complex matrices I1, . . . In, . . . , IN, calledelectromagnetic matrices EM, modeling based on image Ih the lightwavefront propagated along the optical axis for a plurality ofdeviations with respect to the focusing plane of optical system 18, andin particular deviations positioned in the sample.

A method of calculating wavefronts by digital propagation is explainedin Sang-Hyuk Lee et al.'s article entitled “Holographic microscopy ofholographically trapped three-dimensional structures” published inOptics Express, Vol. 15; Nr. 4, Feb. 19, 2017, pp. 1505-1512.

More particularly, noting h_(z)(r) the Rayleigh-Sommerfeld propagationfunction, that is:

${h_{z}(r)} = {{- \frac{1}{2\pi}}\frac{\partial}{\partial z}\frac{e^{i\; \kappa \; R}}{R}}$

where:

z is the so-called “defocusing” height, in other words the deviationwith respect to the focusing plane,

r=(|r|, ∂) is the position in polar coordinates in the image plane, ofradial coordinate |r| and of angular coordinate,

R²=|r|²+z², and

k=2πn/λ is a wave number relative to the propagation medium ofrefraction index n at the wavelength λ of the light source.

Based on this relation, electromagnetic wave a(r, z), of amplitude|a(r,z)| and of phase φ(r,z), in ordinate plane z, can be expressed as:

a(r, z) = a(r, z)exp   (i ϕ(r, z))${a\left( {r,z} \right)} = {\frac{1}{4\pi^{2}}{\int_{- \infty}^{+ \infty}{{B(q)}{H_{- z}(q)}\mspace{14mu} {\exp ({iqr})}d^{2}q}}}$

where

b(r) is the measured intensity, i.e. image Ih (the intensity of thereference wave is here assumed to be constant),

B(q) is th0 e Fourier transform of b(r),

H_(−z)(q) is the Fourier transform of h_(−z)(r), and

q is the dual variable of r in the Fourier transform.

The above equations define an analytic formulation of amplitude a(r, z).Although this model is developed for a propagation in a homogeneousmedium (and thus with no modification of the wave number, without thepresence of an interface creating a reflection and/or a deviation of thewave, etc.), and accordingly with no relation with sample 12 and theenclosure (which comprise many interfaces and changes of index, forexample), the inventors have noted that it enables to reconstruct richelectromagnetic information in relation with the observed particles, aswill be described hereafter.

Thus, advantageously, digital processing means 25 store a single wavenumber, common for all the involved mediums, for example, the index ofair.

As a variation, digital processing means 25 store the refraction indexesand thicknesses of the different involved mediums along the optical axisand constructs matrices I1-IN from close to close to take into accountthe phenomena at the interfaces.

For bacteria, the sampling pitch in the z direction is preferablysmaller than one tenth of the thickness of the bacterium, for example,smaller than 0.1 micrometer, and preferably smaller than 0.03micrometer.

It can thus be understood that a stack of electromagnetic matrices I1-INcan be constructed for ordinates z₁, z₂, . . . , z_(n), z_(N) along theoptical axis, the origin of ordinates (z=0) being taken at the axialfocusing position, each matrix In being defined by a complex amplitudea(r, z_(n)) according to relations:

$\left. {\begin{pmatrix}{a\left( {1,1} \right)}_{z_{n}} & \ldots & {a\left( {c,1} \right)}_{z_{n}} & \ldots & {a\left( {C,1} \right)}_{z_{n}} \\\vdots & \ddots & \vdots & \ddots & \vdots \\{a\left( {1,l} \right)}_{z_{n}} & \ldots & {a\left( {c,l} \right)}_{z_{n}} & \ldots & {a\left( {C,l} \right)}_{z_{n}} \\\vdots & \ddots & \vdots & \ddots & \vdots \\{a\left( {L,1} \right)}_{z_{n}} & \ldots & {a\left( {c,L} \right)}_{z_{N}} & \ldots & {a\left( {C,L} \right)}_{z_{n}}\end{pmatrix}{{\forall{\left( {c,l} \right) \in {\left\lbrack {1,C} \right\rbrack \times \left\lbrack {1,L} \right\rbrack \text{:}{a\left( {c,l} \right)}_{z_{n}}}}} = {a\left( {{r\left( {\left( {c,l} \right),{y\left( {c,l} \right)}} \right)},z_{n}} \right)}}} \right)$

Digital processing means 25 then calculate on each matrix In a positivesurjective application AS from the complex space

^(C×L) to the real space

^(C×L):

${{AS}({In})} = \begin{pmatrix}{{AS}\left( {a\left( {1,1} \right)}_{z_{n}} \right)} & \ldots & {{AS}\left( {a\left( {c,1} \right)}_{z_{n}} \right)} & \ldots & {{AS}\left( {a\left( {C,1} \right)}_{z_{n}} \right)} \\\vdots & \ddots & \vdots & \ddots & \vdots \\{{AS}\left( {a\left( {1,l} \right)}_{z_{n}} \right)} & \ldots & {{AS}\left( {a\left( {c,l} \right)}_{z_{n}} \right)} & \ldots & {{ASD}\left( {a\left( {C,l} \right)}_{z_{n}} \right)} \\\vdots & \ddots & \vdots & \ddots & \vdots \\{{AS}\left( {a\left( {L,1} \right)}_{z_{n}} \right)} & \ldots & {{AS}\left( {a\left( {c,L} \right)}_{z_{n}} \right)} & \ldots & {{AS}\left( {a\left( {C,L} \right)}_{z_{n}} \right)}\end{pmatrix}$

For example, digital processing means 25 calculate the hermitian norm(or its square) of components a(c,l)_(z) _(n) , the absolute value orthe square of the imaginary part (noted Im(a(c,l)_(z) _(n) ) or of thereal part (noted Re(a(c,l)_(z) _(n) ) of components a(c,l)_(z) _(n) , orRe² (a(c,l)z_(n))+Im(a(c,l)_(z) _(n) )) or (Re² (a(c,l)_(z) _(n) )+Im²(a(c,l)_(z) _(n) ))^(1/2).

Without being bound by theory, matrices AS(I1)-AS(IN) do not necessarilyrepresent a light intensity, but the inventors have noted theirresemblance with intensity images obtained under a non-coherentillumination. Particularly, the particles are represented, as in aphotograph, in their particle form.

It is thus possible to apply any type of conventional image processing(segmentation, thresholding, detection of particles based on theirmorphology, etc.), and even for an operator to visually identify theparticles (conversely to an image coding interferences which areintensity-coded in the form of fringes). In the following, to simplifythe notations, matrices AS(I1)-AS(IN) are noted I1-IN, and notationa(c,l)_(z) _(n) correspond to AS(a(c,l)_(z) _(n) ).

The method then comprises identifying particles in the sample accordingto matrices I1-IN, and for each identified particle, determining anoptimal focusing distance z for this particle, and then determining, inthe matrix of series I1-IN corresponding to this distance, a set ofpixels belonging to this particle.

Second unit 52 aims at determining an average focusing distance zfmoyfrom the series of matrices I1-IN and at selecting in this series thematrix, noted Ifmoy, having its distance z equal or the closest todistance zfmoy. As a variation, digital processing means 25 recalculatematrix Ifmoy for distance zfmoy.

Average focusing distance zfmoy is that which best corresponds to theideal conditions of focusing on the set of particles 11 in the sense ofa predetermined focusing criterion. Such a distance can be determined byall known techniques of signal processing or in the field ofphotography, for example, aufocus. The resulting electromagnetic matrixIfmoy is sufficiently “focused” to be able to detect particles atdifferent depths in matrix Ifmoy. The detected particles areparticularly those comprised in a sample depth equal to the depth offield. As previously described, in a preferred embodiment, the particlesare arranged in a volume having a thickness close or equal to this depthof field, so that all or almost all the particles of the sample can bedetected in matrix Ifmoy.

FIG. 3 illustrates an example of determination of the average focusingdistance zfmoy by representing, for each coordinate (c, l), thevariation of a(c,l)_(z) _(n) according to the distance z in the imagestack I1-IN. When a particle is located in sample 12 on the axis,parallel to the optical axis of system 18, of coordinate (c, l) in thefocal plane, a variation of a(c,l)_(z) _(n) can be observed. Forexample, the representation, at 57, of variations a(c,l)_(z) _(n) issimilar to a Gaussian function according to distance z. On the contrary,when no particle is present on this axis, meaning that only the middleof the sample is present, a(c,l)_(z) _(n) does not or only very slightlyvaries. It is thus possible to detect, at 58, an optimum Ipm for eachcoordinate (c, l) representing the specific focusing distance z for thiscoordinate.

Average focusing distance zfmoy can thus be looked for by digitalprocessing means 25 by calculating, at 59, the average of the distancesz obtained by detecting the optimum Ipm of each coordinate (c,l). Ifmoythus is the matrix of the series of matrices I1-IN closest to thecalculated distance z. As a variation, digital processing means 25select the P coordinates, for example, the 10,000 coordinates, havingthe greatest variations of their values a(c,l)_(z) _(n) according to z(for example, having the greatest intervals between the maximum valueand the minimum value), and then calculates the distance zfmoy overthese P coordinates, which increases the accuracy on this distance.

As a variation, the values a(c,l)_(z) _(n) of set P are averaged, andthe optimum of the curve of averaged values according to z iscalculated, the distance z of the optimum being distance zfmoy.

Although the average focusing distance zfmoy illustrates a generalfocusing of the image, the focusing of each particle 11 is not optimal,particularly due to the depth variations of particles 11 relative to oneanother. To improve the focusing on a specific particle 11, theinvention provides determining an optimum focusing distance for eachparticle and determining a focused matrix specific to the particle. Forthis purpose, digital processing means 25 comprise a particle selectionunit 53 and a unit 54 for determining the coordinates of particles 11 inthe image.

Unit 53 of selection of the particles in matrix Ifmoy may take aplurality of image segmentation shapes of the state of the art, such asa scanning of this matrix to detect the contours of a finite element. Asa variation, digital processing means 25 apply a prior thresholding tomatrix Ifmoy, the threshold value being for example equal toMoy(Ifmoy)+p×(Ifmoy), where Moy(Ifmoy) is the average of the pixels ofmatrix Ifmoy, E(Ifmoy) is their standard deviation, and p is an integergreater than 1, for example, equal to 6.

The values greater than this threshold are then determined as belongingto particles, and an image segmentation on the thresholded matrix isimplemented. At the end of the identification, I sets of pixelcoordinates (c,l), noted Part_1, . . . , Part_i, . . . Part_I are thusobtained.

Each set, stored in a memory 26 associated with digital processing means25, records the coordinates in plane X_(n), Y_(n) of the pixels of imageIfmoy belonging to a same particle.

The method then determines, at 54, for each set of coordinates Part_i,which distance z provides the best focusing for the correspondingparticle, and then determines what matrix in series I1-IN corresponds tothis distance (or calculates a new image for this distance), and finallydetermines the coordinates of the particle 11 present in image Ifp.

The calculation of the optimum focusing distance is for exampleperformed similarly to the calculation of the average focusing distance.For each coordinate (c,l) of set Part_i, the distance corresponding tothe optimum of a(c,l)_(z) _(n) is calculated, after which the optimalfocusing distance z is selected to be equal to the average of thecalculated distances z. As a variation, the values a(c,l)_(z) _(n) ofset Part_i are averaged, and the optimum of the curve of averaged valuesaccording to z is calculated, the distance z of the optimum being theselected optimal focusing distance.

The optical focusing distance corresponds to an average focusing onparticle 11, usually resulting in a focusing on a median plane ofparticle 11. Such an average focusing enables to obtain informationrelative to the depth, that is, along axis Z_(n), of particle 11 insample 12. It is thus possible to accurately detect, with no focus, theposition along X_(n), Y_(n) and Z_(n) of a particle 11 in sample 12.

Particles 11 may extend over a plurality of pixels of the image in planeX_(n), Y_(n) and over a plurality of depth units along axis Z_(n). Inthis case, the X_(n), Y_(n), and Z_(n) position of particle 11 in sample12 will be determined according to the center of particle 11.

To focus a laser shot on a particle 11 according to Raman spectroscopy,it is conventional to detect a particle 11 in an image and to displacesample 12 along axis X, X, Y by applying a scale transformation betweenthe position of particle 11 and a real displacement.

The invention provides performing the displacement by means of atriaxial matrix Mc, which is more accurate. Triaxial matrix Mc isobtained, at step 55, by determining the coordinates of at least oneparticle 11 in a plurality of images Ifp according to a plurality ofpredetermined displacements 56. Triaxial matrix Mc aims at modeling thereal displacement performed by sample 12 as a result of a displacementinstruction transmitted by digital processing means 25 to displacementmeans 20 while integrating the opto-mechanical defects of device 10.

As previously described, the different electromagnetic calculations anddisplacements are performed under the assumption of an ideal alignmentof the different reference frames and axes, which induces a differencebetween the real displacements and the displacements desired for sample12 with respect to the detection assembly. A correction is implementedto compensate for this error through a base change matrix Mc enabling totransform the digital position of the particle determined by digitalprocessing means 25 into a real position thereof in the sample.

Triaxial matrix Mc reflects the transformation between the digital spacehaving its values xn, yn, and zn coded in pixels on image Ifp and thereal metric space of the sample displacements relative to the opticalblock, having its values xs, ys, and zs conventionally expressed inmicrometers. Thus, triaxial base change matrix Mc can be expressedaccording to the following relation:

$\begin{pmatrix}{xn} \\{yn} \\{zn}\end{pmatrix} = {{Mc} \times \begin{pmatrix}{xs} \\{ys} \\{zs}\end{pmatrix}}$ ${Mc} = \begin{pmatrix}{Cxx} & {Cxy} & {Cxz} \\{Cyx} & {Cyy} & {Cyz} \\{Czx} & {Czy} & {Czz}\end{pmatrix}$

To determine the coefficients of triaxial matrix Mc, a plurality ofdisplacements are performed and the variation of the position of thesame particle 11 is compared with the displacements instructionstransmitted to displacement means 20.

The number of displacements to be performed may depend on the system tobe qualified and on its properties. At least one displacement perdisplacement axis, be it a rotation or a translation, is to beperformed. It is also possible for the properties of the system toimpose performing a displacement in each displacement direction if thesystem has behavior asymmetries according to the direction, for example,due to a clearance error of the drive system in a given direction.

In particular, in the case of a system provided with three translationaxes and having a behavior asymmetry along each of the axes, sixdisplacements are performed with respect to a central position accordingto the instructions of the stepper motors, for example:

a first displacement to coordinates (0, 0, −30)_(s);

a second displacement to coordinates (+15, 0, −30)_(s);

a third displacement to coordinates (−15, 0, −30)s;

a fourth displacement to coordinates (0, +15, −30)s;

a fifth displacement to coordinates (0, −15, −30)_(s); and

a sixth displacement to coordinates (0, 0, +30)_(s).

In the case of a system provided with three translation axes andprovided with a drive system having no asymmetry, or an asymmetryconsidered as non-prejudicial, it is possible to more simply perform 3displacements only, for example:

a first displacement to coordinates (0, 0, −30)_(s);

a second displacement to coordinates (+15, 0, −30)_(s); and

a third displacement to coordinates (0, +15, −30)_(s).

Further, another displacement may be performed to acquire a backgroundimage enabling to ascertain the quality of the images acquired for eachdisplacement, even in complex cases where many dust particles and debrismask the particles of interest. In particular, a displacement tocoordinates (0, 0, 300)_(s) may be performed to acquire a backgroundimage. As a variation, the background image is acquired only once if thesystem is deemed clean or not varying over time.

In the following, reference is made to the more complex case for asystem with 3 translation axes with an asymmetrical behavior toillustrate the use of the images thus obtained, that is, sixdisplacements.

FIG. 4 illustrates five images Ifp obtained for the first fivedisplacements. The central image Ifp illustrates the particles 11obtained after the first displacement. The circle particle 11 isselected and its coordinates are determined by the previously-describedmethod. The coordinates of particle 11 are stored in memory 26 and thesecond displacement is performed. The right-hand image Ifp illustratesthe second displacement. The 15-micrometer offset along axis X causes adisplacement of particle 11 with respect to the first image Ifp obtainedfor the first displacement. The third displacement guides sample 12along axis X all the way to a −15-micrometer offset with respect to thefirst position. Thus, between the second and the third displacement, thereal distance traveled by sample 12 is 30 micrometers while the otheraxes are invariant.

It is thus possible to simplify the determination of the coefficients oftriaxial matrix Mc according to the following equation:

$\begin{pmatrix}{{xn}\; 1} \\{{yn}\; 1} \\{{zn}\; 1}\end{pmatrix} = {\begin{pmatrix}{Cxx} & {Cxy} & {Cxz} \\\ldots & \ldots & \ldots \\\ldots & \ldots & \ldots\end{pmatrix} \times \begin{pmatrix}30 \\0 \\0\end{pmatrix}}$

The determination of the positions of the circled particle 11 betweenthese two displacements thus enables to obtain coefficients Cxx, Cxy,and Cxz.

Similarly, the fourth and fifth displacements enable to obtaincoefficients Cxy, Cyy, and Czy according to the following simplifiedrelation:

$\begin{pmatrix}{{xn}\; 2} \\{{yn}\; 2} \\{{zn}\; 2}\end{pmatrix} = {\begin{pmatrix}\ldots & \ldots & \ldots \\{Cyx} & {Cyy} & {Cyz} \\\ldots & \ldots & \ldots\end{pmatrix} \times \begin{pmatrix}0 \\30 \\0\end{pmatrix}}$

Similarly, the first and sixth displacements enable to obtaincoefficients Cxz, Cyz, and Czz according to the following simplifiedrelation:

$\begin{pmatrix}{{xn}\; 3} \\{{yn}\; 3} \\{{zn}\; 3}\end{pmatrix} = {\begin{pmatrix}\ldots & \ldots & \ldots \\\ldots & \ldots & \ldots \\{Czx} & {Czy} & {Czz}\end{pmatrix} \times \begin{pmatrix}0 \\0 \\60\end{pmatrix}}$

The resolution of these equation systems thus enables to obtain thecoefficients of triaxial matrix Mc. A matrix Md inverse to triaxialmatrix Mc models the transformation of the pixels into displacements.Inverse matrix Md is expressed according to the following coefficients:

${Md} = \begin{pmatrix}{CORRx} & {CORRxy} & {CORRxz} \\{CORRyx} & {CORRy} & {CORRyz} \\{CORRzx} & {CORRzy} & {CORRz}\end{pmatrix}$

Thus, triaxial matrix Mc or inverse matrix Md exhibits rotations andproportional transformations on all the possible axes. According to anon-limiting example, inverse matrix Md may integrate the followingcoefficients:

${Md} \cong \begin{pmatrix}0.07220 & 0.00040 & {- 0.00129} \\{- 0.00042} & 0.07234 & {- 0.00063} \\0.00034 & {- 0.00019} & 0.10953\end{pmatrix}$

Even if the typical values are low, such values are sufficient tosignificantly alter the results of a measurement by the Ramanspectroscopy having a desired accuracy in the order of 0.07 micrometeralong axes x and y, and 0.02 micrometer along axis z. In the aboveexample, the coefficients are obtained by considering the displacementsof a single particle 11, circled on the images Ifp of FIG. 4.

As a variation, each coefficient may be obtained by an average of thevariations of the coordinates of a plurality of particles 11 present ontwo displacements. Further, a single displacement may be performed ineach direction to obtain triaxial matrix Mc.

When triaxial matrix Mc is known, a displacement instruction may betransmitted by digital processing means 25 to displace sample 12 tofocus laser 17 on a particle of interest 11 having had its positiondetermined as described hereabove. Thus, an accurate laser shot may beperformed on particle of interest 11 while spectrometer 19 captures thediffusion of the light originating from laser 17 to determinecharacteristics, particularly physiological, of particle of interest 11.Further, triaxial matrix Mx may be used several times to determinephysiological characteristics of a plurality of particles of interest11.

Matrix Mc, and thus matrix Md, may be regularly updated, during theintroduction of a sample 12 into the analysis device (for examplerequiring the opening/closing of a drawer or of a door capable ofinducing a displacement of the different parts of the system), or eachtime an analysis of a particle 11 is desired.

The determination of the base change matrix by analysis of the positionof a particle 11 in images has been described. A plurality of particles11 may be analyzed to average the result and obtain a more robustdetermination of matrix Mc.

Similarly, the analysis of the position of a particle, for example, abacterium in a biological sample, has been described. Any type oflandmark, for example, a defect of the medium (for example, a bubble, acrack), may be used to perform the analysis. The description alsomentions a stage 20 to displace sample 12 by means of stepper motors. Asa variation, other displacement means may be implemented and thedisplacements may be performed manually by an operator. The matchingmatrix then indicates to the operator the accurate displacements to beperformed to target a particle 11 in sample 12.

1. A method of calibration of a device for analyzing at least oneelement present in a sample, said device comprising: a detectionassembly comprising a light source configured to illuminate said sample,an optical system configured to collect a light radiation originatingfrom said sample, and a planar image sensor configured to acquire aholographic image formed by the interference between a reference waveoriginating from said light source and a wave diffracted by saidradiation originating from the sample; and digital processing meansconfigured to detect a digital position of at least one element in saidsample based on said acquired holographic image, and to calculate a realposition of said element according to said digital position and to adigital position and real position matching model; wherein thecalibration method comprises implementing a plurality of predetermineddisplacements of said sample with respect to said optical system and,for each of said displacements, detecting a digital position of a sameelement to determine said digital position and real position matchingmodel according to the predetermined displacements and to the digitalpositions of said element after each displacement, said detectioncomprising the steps of: acquiring an image; digitally constructing aseries of electromagnetic matrices modeling, by digital propagation ofsaid acquired holographic image, the electromagnetic wave in planesparallel to the plane of the image sensor and comprised in said samplefor a plurality of differences with respect to said plane; based on theseries of electromagnetic matrices, determining an average focusingmatrix for said sample and determining the corresponding electromagneticmatrix; identifying said same element in the first correspondingelectromagnetic matrix; and determining said digital position of saidsame element in said electromagnetic matrix; said digital position andreal position matching model corresponding to a triaxial matrix alongthree axes of a metric system, said step of determining said digitalposition of said same element in said electromagnetic matrix beingcarried out along an axis, modeling the position of said element in thedepth of said sample, according to said electromagnetic matrix at theaverage focusing distance of said sample.
 2. The calibration methodaccording to claim 1, wherein the predetermined displacements areperformed in two opposite directions for each axis of said metricsystem.
 3. The calibration method according to claim 1, wherein thedetermination of the digital position and real position matching modelis performed via an average of the variations of the digital positionsof a plurality of elements present in said holographic image.
 4. Thecalibration method according to claim 1, wherein said optical system hasan optical axis A_(OPT) and performs the conjugation between a focusingplane and a focal plane, wherein the step of acquisition of saidholographic image is carried out while said optical system is placedwith respect to said sample in such a way that said elements of saidsample are not in said focusing plane.
 5. The calibration methodaccording to claim 1, wherein before the steps of acquisition of aholographic image to obtain said digital positions of said element, themethod comprises a step of acquisition of a background image, theholographic images obtained during said acquisition steps beingnormalized by said background image.
 6. The calibration method accordingto claim 1, wherein said element corresponds to a landmark of saidsample.
 7. The calibration method according to claim 1, wherein saidelement corresponds to a particle present in said sample.
 8. Thecalibration method according to claim 7, wherein the step of determiningsaid digital position of said particle in said electromagnetic matrix isperformed by looking for the center of said particle.
 9. The calibrationmethod according to claim 7, wherein the matching model between digitalpositions and real positions is formed by considering a plurality ofparticles present in said sample, the digital positions of the particlesbetween two consecutive images being determined by looking for thepositions of the particles of said two images, by calculating thevectors coupling the particles two by two and by determining a probabledisplacement vector corresponding to the most recurrent vector.
 10. Adevice for analyzing at least one element present in sample, said devicecomprising: a detection assembly comprising a light source configured toilluminate said sample, an optical system configured to collect thelight radiation originating from said sample, and a planar image sensorconfigured to acquire a holographic image formed by the interferencebetween a reference wave originating from said light source and a wavediffracted by said radiation originating from the sample; and digitalprocessing means configured to detect a digital position of at least oneelement in said sample based on said acquired holographic image and tocalculate a real position of said element according to said digitalposition and to a digital position and real position matching model;means for displacing the sample with respect to the optical system, saiddisplacement means being driven by the digital processing means; whereinthe digital processing means are configured to control the displacementmeans to perform a plurality of predetermined displacements of saidsample with respect to said optical system and, for each of saiddisplacements, to detect a digital position of a same element todetermine said digital position and real position matching modelaccording to the predetermined displacements and to the digitalpositions of said element after each displacement, the detection of thedigital position comprising the steps of: acquiring a holographic image;digitally constructing a series of electromagnetic matrices modeling, bydigital propagation of said acquired holographic image, theelectromagnetic wave in planes parallel to the plane of the image sensorand comprised in said sample for a plurality of deviations with respectto said plane; based on the series of electromagnetic matrices,determining an average focusing matrix for said sample and determiningthe corresponding electromagnetic matrix; identifying said same elementin the first corresponding electromagnetic matrix; and determining saiddigital position of said same element in said electromagnetic matrix.11. A device for analyzing at least one element present in sample, saiddevice comprising: a detection assembly comprising a light sourceconfigured to illuminate said sample, an optical system configured tocollect the light radiation originating from said sample, and a planarimage sensor configured to acquire a holographic image formed by theinterference between a reference wave originating from said light sourceand a wave diffracted by said radiation originating from the sample; anddigital processing means configured to detect a digital position of atleast one element in said sample based on said acquired holographicimage and to calculate a real position of said element according to saiddigital position and to a digital position and real position matchingmodel; means for displacing the sample with respect to the opticalsystem, said displacement means being driven by the digital processingmeans; wherein the digital processing means are configured to controlthe displacement means to perform a plurality of predetermineddisplacements of said sample with respect to said optical system and,for each of said displacements, to detect a digital position of a sameelement to determine said digital position and real position matchingmodel according to the predetermined displacements and to the digitalpositions of said element after each displacement, the detection of thedigital position comprising the steps of: acquiring a holographic image;digitally constructing a series of electromagnetic matrices modeling, bydigital propagation of said acquired holographic image, theelectromagnetic wave in planes parallel to the plane of the image sensorand comprised in said sample for a plurality of deviations with respectto said plane; based on the series of electromagnetic matrices,determining an average focusing matrix for said sample and determiningthe corresponding electromagnetic matrix; identifying said same elementin the first corresponding electromagnetic matrix; and determining saiddigital position of said same element in said electromagnetic matrix,wherein the digital processing means are configured to implement themethod according to claim 1.